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First, let's call the point at the right angle "D", so BD + DC = BC
Well, since angle B is 60, then angle A is 30, and the side across from the 30 degree angle in a 30-60-90 triange is always half of the hypoteneuse. So that makes BD = .5
Now, the longer leg in a 30-60-90 triangle is sqrt(3) times the shorter leg, so AD is .5 * sqrt(3). Because triangle ADC is a 45-45-90 triangle, then AD = DC = .5 * sqrt(3). so BC is .5 + .5 * sqrt(3).